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IEOR162_HW1_Solution

IEOR162_HW1_Solution - IEOR 162 Spring 2009 Solution for...

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IEOR 162, Spring 2009, Solution for Homework 1 2.1.2 y y y 3 2 1 = 60 . 30 . 20 . 30 . 70 . 30 . 10 . 0 50 . x x x 3 2 1 2.1.4 The i j'th element of (AB) T = element j i of AB, = Scalar product of row j of A with column i of B. Now element i j of B T A T = Scalar product of row i of B T with column j of A T = Scalar product of row j of A with column i of B. Thus, (AB) T = B T A T . 2.2.1 3 1 1 2 1 1 x x 2 1 = 8 6 4 and 1 1 4 2 1 6 1 3 8 2.3.2 6 4 0 2 1 1 1 1 2 4 1 1 0 1 1 1 2 2 1 1 0 2 0 1 This system has an infinite number of solutions of the form x 3 = k, x 1 = 2 2k, x 2 = 2 + k. 2.3.6 0 2 2 4 1 2 1 4 0 1 1 0
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